On computational proofs of the existence of solutions to nonlinear parabolic problems

This paper is an extension of the preceding study (Nakao, this journal, 1991) in which we described a numerical verification method of the solution for one-space dimensional parabolic problems, to the several-space dimensional case. Here, numerical verification means the automatic proof of the existence of solutions to the problems by some numerical techniques on a computer. We reformulate the verification condition for nonlinear parabolic initial boundary value problems using the fixed-point problem of a compact operator on certain function spaces. As in the preceding study based upon a simple C⁰ finite-element approximation and its constructive a priori error estimates, a numerical verification procedure is presented with some numerical examples.     

Activity of SiDbCl in the Electrooxidation of Ascorbic Acid,Dopamine, and Uric Acid

Selective electroanalytical responses for ascorbic acid, dopamine and uric acid at a carbon modified electrode based on 3‐n‐propyl‐1‐azonia‐4‐azabicyclo[2.2.2]octane silsesquioxane chloride (SiDbCl) is reported. The overlapped peaks observed at an unmodified electrode are resolved into three well defined voltammetric peaks allowing the simultaneous determination of the three species. Detection limits of 37, 0.3 and 0.1 μmo L⁻¹ of ascorbic acid, dopamine and uric acid, respectively, were calculated from calibration curves based on differential pulse voltammetric experiments performed in Britton ‐ Robinson buffer solution at pH 7.04.     

Structural study of a series of layered rare-earth hydroxide sulfates

We report structure analysis of a new family of rare-earth hydroxides Ln(2)(OH)(4)SO(4)·2H(2)O (Ln = Pr, Nd, Sm, Eu, Gd, Tb) from synchrotron X-ray and electron diffraction data. Rietveld profile analysis revealed that all members were isostructural and crystallized in a face-centered monoclinic system A2/m (No. 12), in which the monoclinic angles were approximately equal to the right angle, varying from 90.387(1)° for Pr sample to 90.0718(3)° for Tb sample. The structure consisted of LnO(9) polyhedra connected by μ(3)-hydroxyl groups and μ(2)-water molecules, forming a corrugated two-dimensional layer, which was pillared by bidentated sulfate ions. This series of compounds had a supercell a' = 2a, b' = 2b because of the local orientation ordering of SO(4)(2-). Structural features along the series, such as unit-cell parameters and average Ln-O distances, represented a progressive contraction associated with the shrinking radius of the lanthanide cations from Pr to Tb.     

All-Fiber Optical Add-Drop Multiplexer Using a Pair of Fiber Grating Couplers

A new all-fiber optical add-drop multiplexer (ADM) using a pair of fiber grating couplers (FGCs) was proposed and first demonstrated. It was theoretically and experimentally shown that both drop and add efficiencies could be maximized in the proposed ADM. It was also clarified that the crosstalk between dropped and added signals could be improved in the proposed ADM compared with that in the single FGC. Drop and add operations in the ADM for 3-channel WDM signals with 1.6 nm wavelength spacing were confirmed. The ADM with signal amplification ability, which consists of a pair of FGCs, an EDF, and a pump-LD, was proposed and demonstrated. It was confirmed that the dropped and transmitted optical signals could be amplified in the ADM, and would be able to expand fiber routing spans.     

Chemical synthesis and application of C-terminally 5-carboxyfluorescein-labelled thymopentin as a fluorescent probe for thymopoietin receptor.

Thymopentin (TP5) is a synthetic pentapeptide fragment, which corresponds to position 32 - 36 of thymic polypeptide thymopoietin. Thymopoietin and TP5 display a variety of biological functions, including phenotypic differentiation of T cells and the regulation of immune systems. Previous chemical modification experiments suggested that there was an absolute requirement for N-terminal amino acids to maintain the biological activity of TP5. On the basis of this structure-activity relationship, we designed and synthesized the C-terminally 5-carboxyfluorescein-coupled TP5 (TP5-FAM) as a fluorescent probe for thymopoietin receptor. TP5-FAM could bind to the membrane of human lymphoid cell lines, MOLT-4 cells, in which the thymopoietin receptor is expressed. The binding is specific and saturable (K(d) = 33 microM). TP5 and human splenopentin are nearly equipotent inhibitors of TP5-FAM binding to the thymopoietin receptor, but porcine secretin did not show any significant inhibition of TP5-FAM binding to MOLT-4 cells. Thus, TP5-FAM is suggested to be a potent and biologically active ligand that would be useful for studying the binding and functional characteristics of the human thymopoietin receptor.     

Determination of peptide φ angles in solids by relayed anisotropy correlation NMR

A solid state NMR method is presented for determination of a backbone dihedral angle φ in peptides, being based on the previously reported method, relayed anisotropy correlation (RACO) NMR [Y. Ishii et al., Chem. Phys. Lett. 256 (1996) 133]. In the present method, the and the dipolar tensors in the system are two-dimensionally (2D) correlated via polarization transfer from to under magic angle spinning (MAS). This method was applied to N-acetyl , -valine, and the H–C–N–H dihedral angle was determined to be 154.0±1.4° or 206.0±1.4°, the former agreeing with the X-ray value of 154±5°.     

Mössbauer spectroscopic study of frozen solutions of57Co using a specially designed cryostat for time differential coincidence emission Mössbauer spectroscopy of237Np

Experiments on the⁵⁷Fe Mössbauer effect in frozen solutions were carried out in order to demonstrate the capabilities of a cryostat which was developed for the emission Mössbauer spectroscopy of²³⁷Np. We confirmed the existence of an aliovalent state of⁵⁷Fe in the temperature range from 5.5 to 35 K. However, the relative amounts of Fe(II) and Fe(III) in the frozen matrix were almost constant for the temperature range from 5.5 to 150 K. The design, operation and capabilities of the cryostat are also described.